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The Poisson-exponential model for recurrent event data: an application to bowel motility data

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  • Francisco Louzada
  • M�rcia A.C. Macera
  • Vicente G. Cancho

Abstract

This paper presents a new parametric model for recurrent events, in which the time of each recurrence is associated to one or multiple latent causes and no information is provided about the responsible cause for the event. This model is characterized by a rate function and it is based on the Poisson-exponential distribution, namely the distribution of the maximum among a random number (truncated Poisson distributed) of exponential times. The time of each recurrence is then given by the maximum lifetime value among all latent causes. Inference is based on a maximum likelihood approach. A simulation study is performed in order to observe the frequentist properties of the estimation procedure for small and moderate sample sizes. We also investigated likelihood-based tests procedures. A real example from a gastroenterology study concerning small bowel motility during fasting state is used to illustrate the methodology. Finally, we apply the proposed model to a real data set and compare it with the classical Homogeneous Poisson model, which is a particular case.

Suggested Citation

  • Francisco Louzada & M�rcia A.C. Macera & Vicente G. Cancho, 2015. "The Poisson-exponential model for recurrent event data: an application to bowel motility data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2353-2366, November.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:11:p:2353-2366
    DOI: 10.1080/02664763.2015.1030369
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    References listed on IDEAS

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    1. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    2. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    3. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
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